In a medium-sized sauce pan over medium heat, combine the whole milk and butter. Stir the two together until the butter has completely melted. Set the pan aside so the mixture cools to luke warm (you don't need to use a thermometer - but anywhere between 100-110 degrees Fahrenheit is perfect!). It just cannot be hot.
While the milk/butter mixture is cooling, add the warm water (luke warm, not hot) with the two packages of instant yeast to the bowl of a stand mixer and whisk together until combined.
Once the milk/butter mixture is cooled, pour it into the stand mixer with the water/yeast mixture.
Lightly beat the eggs and add that to the mixture. Add the granulated sugar, ground nutmeg, salt, and half of the flour (about 2 ½ cups or 325 grams). Using the paddle attachment, mix all of the ingredients together on low speed for 30 seconds. Turn the mixer up to medium speed and mix until well combined.
Add the remaining flour and mix together on low speed for 30 seconds, then turn the mixer up to medium speed and mix until combined. Switch out the paddle attachment for the hook attachment, and beat the dough for 3-4 minutes. The dough will slightly pull away from the sides of the bowl, however it WILL be a wet and sticky dough. Do not add more flour - I promise!!! You will want to, but don't.
Transfer the dough to a well oiled bowl, cover it with a towel, and let the dough rise in a warm environment (oven or microwave turned OFF are always good choices) for one hour. It will double in size.
Once the dough has doubled in size, gently move it to a lightly floured surface. Roll the dough out slightly until it is about ½ inch thick. Divide the dough into 16 equal pieces and shape them into balls.
Place the donuts on a lightly floured pan, cover it with a towel, and let the dough rise for an additional 30-40 minutes.
In the last 10 minutes of the dough's second rise, begin to heat up your oil. Pour the oil into a large pot so there is at least 2-3 inches of oil. Using a thermometer, heat the oil to about 365 degrees Fahrenheit and monitor the temperature the entire time. Make sure the thermometer is submerged in the middle of the oil and not touching the bottom of the pan (it will read hotter if the thermometer is touching the pan).
Once the dough is done with the second rise, fry them. Place 2-3 donuts in the pot at once (do not overcrowd) and fry them for one minute on each side until golden brown. Remove the donuts from the oil and place them on a pan lined with paper towels to soak up the excess oil. Repeat this process with all of the donuts.